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Potential NRQCD and Heavy-Quarkonium Spectrum at Next-to-Next-to-Next-to-Leading Order

B. A. Kniehl·A. A. Penin·V. A. Smirnov·M. Steinhauser
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Abstract

The next-to-next-to-next-to-leading order (N^3LO) Hamiltonian of potential nonrelativistic QCD is derived. The complete matching of the Hamiltonian and the contribution from the ultrasoft dynamical gluons relevant for perturbative bound-state calculations is performed including one-, two-, and three-loop contributions. The threshold expansion is used to disentangle and match contributions of different scales in the effective-theory calculations. As a physical application, the heavy-quarkonium spectrum is obtained at N^3LO for the case of vanishing QCD beta function. Our results set the stage for a full N^3LO analysis of the heavy-quarkonium system.

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B. A. Kniehl, A. A. Penin, V. A. Smirnov, M. Steinhauser. 2002-03-18. Potential NRQCD and Heavy-Quarkonium Spectrum at Next-to-Next-to-Next-to-Leading Order. https://doi.org/10.1016/s0550-3213(02)00403-0

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